Participants 2019

Saad Raza

Name  

Saad Raza

University

COMSATS University Islamabad

Supervisor

Prof. Dr. Peter Bastian

Workgroup  

Parallel Computing

Project

The Navier-Stokes equations and its implementation on Image inpainting

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At IWR, I have carried out research on the project “The Navier-Stokes equations and its implementation on Image inpainting ” under the supervision of Prof. Dr. Peter Bastian.  In past, there has been a lot of research in the field of image inpainting  by using partial differential equation. In this project, we take the 2D-NSE equation to implement on image inpainting. The main goal of the project was to achieve the improve algorithm for inpainting  based on finite element method. Improvement in algorithm is judged on the basis of algorithm accuracy, efficiency, and stability. For numerical implementation of our algorithm, I have used the Distributed and Unified Numerics Environment (Dune) software. Besides this I also take part in other academic activities. I participated in the workshop "Markov Chain Monte Carlo for Inverse Problems in PDEs" by Prof. Colin Fox (Romberg Visiting Scholar 2018). I also participated in some recreational activities including university summer trips which gives me the brief idea about German rich and historical culture. Nonetheless my stay at HGS MathComp is very fruitful both academically and socially.

Jiaxuan Sun

Name  

Jiaxuan Sun

University

University Huazhong University of Science and Technology

Supervisor

Prof. Dr. Vincent Heuveline

Workgroup 

Engineering Mathematics and Computing Lab (EMCL)

Project

Data analysis based on computing time and power measurement of Multigrid linear solver on Multi-GPU

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When talking about High Performance Computing, not only the performance but also the energy consumption would influence the efficiency of the program. Currently, EMCL is working on a project named Mekong, which the main objective is to provide a simplified path to scale out the execution of GPU programs from one GPU to almost any number. And the mini-app, which consists of several applications that are solvable by using GPU computation, is a demo for how the idea works. We use CUDA to program the GPU functions and NVML to measure the time and energy consumption of kernels. By collecting data from running the program, the analysis would lead to a platform for the joint evaluation of both compute performance and energy consumption. The chance to participate in this program is fantastic, during which I experienced actual research life and comfortable living environment in Heidelberg, and it couldn’t happen without acceptance and supervision from Prof. Vincent Heuveline and grateful help from EMCL colleagues. I would also thank HGS MathComp for the best platform they provide.

Anima Kujur (JNU)

Name  

Anima Kujur

University

JNU, New Delhi, India

Supervisor

Dr. Michael Winckler

Workgroup  

HGS MathComp core unit

Project

Modelling of Dynamical Systems with System of
Ordinary Differential Equations and Numerical
Approximation of Derivatives

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At IWR, I have carried out two research projects.

The first project was “Modelling of Dynamical Systems with System of Ordinary Differential Equations.” For this I have taken a benchmark dynamical system which represents the real world problem.

The goal was to approximate the solution with minimum relative error. With the help of two numerical methods (Euler explicit method and Euler Richardson method) I approximated the solution and compared the simulation results. I studied the convergence rate of the two methods and numerically showed the faster convergence of the Euler-Richardson-method over the Explicit-Euler-Scheme.

The second project was ”Numerical Approximation of Derivatives. ” The aim of this project was to approximate the derivative for an unknown function. For this project I have used secant method in two versions (one sided and symmetric difference quotients) to compute the derivative for a benchmark problem. The two sided version of secant method gives the good approximation.

It was a wonderful opportunity to improve my academic skills.

I am very grateful to Dr. Michael Wincker and the entire team for giving me a chance to be a part of Post- Bachelor Program. It was a lifelong memory.